A student applies a force of magnitude 39.0 N at an angle of 22.6o with the horizontal to push a

4.00-kg textbook 1.00 m across a table from rest to a final speed of 1.75 m/s. Find the work
done by friction on the textbook.

See the answers posted at

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to the same question.

To find the work done by friction on the textbook, we need to understand the concept of work and the work-energy principle.

Work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. Mathematically, work (W) can be expressed as:

W = F * d * cosθ

where:
- W is the work done
- F is the applied force
- d is the displacement of the object
- θ is the angle between the applied force and the direction of displacement

In this case, the work done by the friction force can be calculated using the above formula. However, we first need to find the force of friction acting on the textbook.

The force of friction can be calculated using the equation:

f_friction = μ * N

where:
- f_friction is the force of friction
- μ is the coefficient of friction
- N is the normal force

Since the textbook is on a horizontal surface, the normal force (N) is equal to the weight of the textbook, which can be calculated using:

N = m * g

where:
- m is the mass of the textbook
- g is the acceleration due to gravity (approximately 9.8 m/s^2)

Now, we have all the information needed to calculate the work done by friction.

1. Calculate the normal force (N):
N = m * g
N = 4.00 kg * 9.8 m/s^2
N = 39.2 N

2. Calculate the force of friction (f_friction) using the coefficient of friction (μ):
You haven't provided the coefficient of friction, so you'll need to look it up or assume a value to proceed with the calculation. Let's say the coefficient of friction is 0.3 (as an example).

f_friction = μ * N
f_friction = 0.3 * 39.2 N
f_friction = 11.76 N

3. Calculate the work done by friction (W):
We can now use the formula for work to find the value of W. The force of friction acts opposite to the direction of motion, so the angle between the force of friction and the displacement is 180 degrees (cos 180 = -1).

W = f_friction * d * cosθ
W = 11.76 N * 1.00 m * cos 180
W = -11.76 J

Therefore, the work done by friction on the textbook is -11.76 Joules. The negative sign indicates that the work is done against the motion of the textbook.